Contemporary Mathematics Topic 7 Truth Tables Truth Values

Contemporary Mathematics Topic 7: Truth Tables

Truth Values and Truth Tables › We regard the truth values of a statement as either True (T) or False (F). › “George Washington was a United States President. ” is a True statement, so it is assigned a truth value of T. › “All cats are dogs. ” is a False statement, so it is assigned a truth value of F. › We can arrange truth values into a table showing all possible values of a statement – this is called a truth table.

Conjunctions › Recall that a conjunction is a statement combining two smaller statements using the word “and” usually. › Here is the truth table for conjunctions: P Q T T F F F T F F › Hence, conjunctions are “true” only when both statements are also true.

Disjunctions › There are two types of disjunctions (“or” statements) – inclusive and exclusive. We will focus only on the inclusive. › Here is the truth table for (inclusive) disjunctions: P Q T T F F F › Hence, disjunctions are true whenever either statement is true.

Negations › A negation changes the truth value of a statement. › The truth table for negations: P ~P T F F T › Hence, a negation will always swap the truth value. This is used in many different truth statements and tables.